Botanist Robert Brown discovered the random motion of pollen in water in 1827. He hypothesized that it was the smallest living organism.

His hypothesis was incorrect. The pollen was small enough that the molecules of water were contacting it and changing its direction.

In 1905 Einstein published a paper on modeling the motion of pollen in water.

Ito Calculus is an extension of differential calculus to include stochastic processes.

Black and Scholes model is the first non-deterministic stock option pricing model. The authors won the Nobel prize in 1997 for the work on this model. It assumes stocks move along with the risk free interest rate, they added in a variable for random noise ( in the form of a Normal distribution ) which is based on Brownian motion. The noise modeled future news releases.